mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

x to the power of x

If \(x^{x^{x^{x^{...}}}}\) [\(x\) to the power of (\(x\) to the power of (\(x\) to the power of (\(x\) to the power of ...))) with an infinite number of \(x\)s] is equal to 2, what is the value of \(x\)?

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths IV,
puzzles about algebra, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

lines graphs surds sequences triangles pentagons perimeter taxicab geometry digits expansions volume doubling spheres triangle numbers star numbers tiling digital products integration algebra range multiplication trigonometry ave routes averages means powers pascal's triangle tangents crosswords factorials palindromes christmas balancing cube numbers cards coordinates scales consecutive numbers crossnumbers cubics multiplaction squares decahedra fractions dice multiples money complex numbers elections prime factors menace square roots coins shapes lists chess dominos calculus differentiation numbers chocolate odd numbers probabilty cryptic clues remainders dodecagons factors logic addition games xor squares angles rugby chalkdust crossnumber sport circles wordplay unit fractions even numbers division polygons regular shapes grids combinatorics cryptic crossnumbers integers tournaments albgebra speed matrices square grids median products symmetry binary folding tube maps bases prime numbers gerrymandering hexagons sums 2d shapes square numbers books shape clocks planes sets mean advent quadrilaterals ellipses 3d shapes floors irreducible numbers people maths sum to infinity area perfect numbers medians proportion functions parabolas percentages the only crossnumber probability neighbours number consecutive integers colouring geometry geometric mean determinants arrows quadratics polynomials time axes geometric means partitions rectangles digital clocks indices dates

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026